Entanglement manipulation and distillability beyond LOCC

TL;DR

This paper explores generalized entanglement resource theories beyond LOCC, revealing new properties of entanglement manipulation, superactivation phenomena, and state convertibility under broader classes of quantum channels.

Contribution

It introduces and analyzes classes of channels beyond LOCC, such as dually non-entangling and PPT-preserving channels, and demonstrates their impact on entanglement distillation and state convertibility.

Findings

Non-entangling maps can be superactivated to create entanglement.

Every NPT entangled state can be made LOCC-distillable with certain channels.

Any two multipartite pure states can be interconverted via polytope approximations to separable channels.

Abstract

When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex leaving many important physical problems unsolved. In this paper we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and PPT-preserving channels. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We first show that unlike LOCC, general non-entangling maps can be superactivated, in the sense that two copies of the same non-entangling map can nevertheless be entangling. On the single-copy level, we demonstrate that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and that every state can be converted into an LOCC-distillable state using operations belonging to any family of polytopes that approximate LOCC. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable channels. Finally, as an analog to $k$-positive maps, we introduce and analyze the set of $k$-non-entangling channels.